Jon Pace & the Latest Prime Number

In case you missed it, the world has a new largest prime number called M77232917:

46733318335923109998833558556111552125132110281771449579858233859356792348052117720748431109974020884962136809003804931724836 … and on and on and on for another 23,249,300 digits.

That number is unimaginably large. It is so large that even analogies meant to help us wrap our minds around it are nearly unimaginable. Who can imagine a number that takes up 9,000 pages? Or imagine a number that stretches 73 miles?[1] Or imagine writing 5 digits per second for 54 days? Such are the ways tries to describe the number. (I might add, parenthetically, has the nicest website 1996 can buy).

The Great Internet Mersenne Prime Search page is Internet Retro at its finest.

The history of prime numbers in general is fascinating as is the history of Mersenne primes in particular. But I will save those for another post. Here I just want to draw attention to how the newly recognized prime status of this number has been noted in the press.[2] In particular, I’m intrigued by how different reports apportion credit for the “discovery” and how they describe Jon Pace, whose computer first identified the number as prime.

We might as well start with the post at that announces: GIMPS Project Discovers Largest Known Prime Number: 277,232,917–1. In case there was any doubt that the GIMPS project wanted to take credit for the discovery, the post continues:

The Great Internet Mersenne Prime Search (GIMPS) has discovered the largest known prime number, 277,232,917–1, having 23,249,425 digits. A computer volunteered by Jonathan Pace made the find on December 26, 2017. Jonathan is one of thousands of volunteers using free GIMPS software available at … GIMPS, founded in 1996, has discovered the last 16 Mersenne primes.

Make no mistake, GIMPS discovered this latest prime, along with the previous 16 Mersenne primes. And although Jon Pace installed and ran the software on his computer, the result had to be checked by four other people who also deserve credit. Oh, and credit goes to all the people who didn’t find a prime. Credit for the discovery, in this version, echoes the distributed nature of the labor but reserves pride of place for the GIMPS software and its developer:

GIMPS Prime95 client software was developed by founder George Woltman. Scott Kurowski wrote the PrimeNet system software that coordinates GIMPS’ computers. Aaron Blosser is now the system administrator, upgrading and maintaining PrimeNet as needed. …
Credit for this prime goes not only to Jonathan Pace for running the Prime95 software, Woltman for writing the software, Kurowski and Blosser for their work on the Primenet server, but also the thousands of GIMPS volunteers that sifted through millions of non-prime candidates. In recognition of all the above people, official credit for this discovery goes to “J. Pace, G. Woltman, S. Kurowski, A. Blosser, et al.”

Thanks for the CPU cycles and paying for the electricity to run your computer, Jon. But don’t feel slighted, GIMPS tends to celebrate its software over the people donating the computer time.

Who is this Jon Pace, well GIMPS say simply “Jonathan Pace is a 51-year old Electrical Engineer living in Germantown, Tennessee.” A nice, reasonable, scientific sounding person.

Science Daily just reposts the GIMPS report, changing the title slightly: “Largest known prime number discovered 50th known Mersenne prime ever found, on computer volunteered in collaborative project.”

Things begin to drift in the NPR story, “A Tenn. Man Recently Discovered The Largest Prime Number Known To Humankind.” Perhaps we shouldn’t be surprised that NPR with its preference for the human-interest story would highlight Jon Pace:

This past week, a FedEx employee from Germantown, Tenn., made a massive discovery — and it wasn’t in any packages. John Pace found the largest prime number known to humankind. …
Pace found his prime as part of an online collective called the Great Internet Mersenne Prime Search, or GIMPS. Pace and thousands of volunteers ran software on their personal computers crunching numbers day-in and day-out.

In this version, Pace discovered the prime and, moreover, its “his prime” (later the article refers to it as “Pace’s prime”). Not only is Pace the only one to get credit for the discovery, he is no longer an electrical engineer. Instead, he’s a FedEx employee. The two are by no means mutually exclusive. I am not suggesting they are. I am, rather, drawing attention to the fact that in the NPR version Pace’s primary marker of identity is his status as a FedEx employee whereas in the GIMPS post his primary identity is as an electrical engineer.

Popular Science adds a bit more to the story, “How a FedEx employee discovered the world’s largest prime number.” In this version Pace gets credit for the discovery, that he used the GIMPS software is just part of the process.

What does change in this version is Pace’s identity. Now he’s not only a FedEx employee—“a flight operations finance manager with the Memphis-based delivery behemoth”— but also a deacon at his church, the Germantown Church of Christ where he does, among other things, IT support. He installed the GIMPS software on one of the computers at the church.

Yes, Jon Pace is a Deacon at the Germantown Church of Christ, for whatever that’s worth.

The NY Times shifts the emphasis again: “How a Church Deacon Found the Biggest Prime Number Yet (It Wasn’t as Hard as You Think).” By this point, Pace is given sole credit for having discovered the prime number. Equally interesting, his identity has shifted to emphasize his role as a deacon at the Germantown Church of Christ:

A prime number discovery in December was made in the unlikeliest of places: on a church computer in a Memphis suburb.…
But for this behemoth to come to light, someone had to have installed free software used to search for Mersenne prime numbers, and that someone is Jon Pace, a deacon, FedEx finance manager and math aficionado who had spent 14 years hunting for such a number.

According to the article, Pace is prouder of “the 20 years [he has] served as deacon at Germantown” than of discovering the new prime number.

Discovery appears to be a rather slippery concept. What does it mean to discover a prime number? In what sense do numbers exist or not exist before we write them down? Surely nobody is suggesting the number 277,232,917–1 was discovered. But its primeness was discovered, or perhaps realized. In this case, discovery seems to be rather traditional, like discovering gold or the New World. Something pre-existed in some way before a human stumbled into it, but the identity, characteristics, and value of that something had to be recognized before we could talk about it and apportion credit. Here we see GIMPS asserting credit for the “discovery” whereas NPR or the NY Times are perfectly happy to give Pace the credit. Credit for the discovery is ambiguously related to labor—GIMPS thinks the intellectual labor that created the software more important than the volunteer labor (and donated electricity and other operating expenses); the NY Times thinks the human who owns the donated computer and pays to operate them more important.

And what about that human, in this case Jon Pace? GIMPS emphasizes Pace’s identity as an electrical engineer, though electrical engineering is only one part of his identity—along with his undergraduate degree in electrical engineering he has an M.B.A., is a flight operations finance manager,[3] and is a deacon at his church. And according to the NY Times, he is most proud of being a deacon. How is Pace’s reported identity related to the values different organizations hold? How does Pace’s identity as an electrical engineer reinforce the image that GIMPS wants to project? Why does Popular Science and the NY Times draw attention to Pace’s identity as a deacon in a church? I don’t believe that GIMPS didn’t know Pace was a deacon, though they chose not to acknowledge that aspect of his identity. The NY Times, by contrast and somewhat surprisingly to me, chose to draw attention to Pace’s work as a deacon at his church.

Discovery, it turns out, is pretty difficult to pin down.

  1. I suspect most people can identify cities that are roughly 73 miles apart but have no concept of what that distance actually is (FYI, it’s about 73 miles from Haverford College to the New Jersey shore, e.g., Ocean City). Now remove the bookending cities and challenge people to think about 73 miles of highway stretching through undulating grasslands or through the desert—suddenly the distance becomes meaningless. And how are we supposed to relate to 73 miles? A person walking will have a very different relationship to that distance than a person who thinks of driving it.  ↩

  2. And yes, that tortured expression, “newly recognized prime status” was intentional, an effort to avoid words like “discovered” and “found,” and an effort to draw attention to what strikes me as interestingly new here, i.e., our recognition that this number has a set of features that we call prime.  ↩

  3. I confess, I have no idea what a flight operations finance manager is. Flight operations manager I can imagine. Finance manager again makes sense. The two together, however, confuse me.  ↩